Effects of particle size on crushing and deformation behaviors of rockfill materials

Strength and deformation behaviors of rockfill materials,key factors for determining the stability of dams,pertain strongly to the grain crushing characteristics.In this study,single-particle crushing tests were carried out on rockfill materials with nominal particle diameters of 2.5 mm,5 mm and 10 mm to investigate the particle size effect on the single-particle strength and the relationship between the characteristic stress and probability of non-failure.Test data were found to be described by the Weibull distribution with the Weibull modulus of 3.24.Assemblies with uniform nominal grains were then subjected to one-dimensional compression tests at eight levels of vertical stress with a maximum of 100 MPa.The yield stress in one-dimensional compression tests increased with decreasing the particle size,which could be estimated from the single-particle crushing tests.The void ratio-vertical stress curve could be predicted by an exponential function.The particle size distribution curve increased obviously with applied stresses less than 16 MPa and gradually reached the ultimate fractal grading.The relative breakage index became constant with stress up to 64 MPa and was obtained from the ultimate grading at the fractal dimension(a?2:7).A hyperbolical function was also found useful for describing the relationship between the relative breakage index and input work during one-dimensional compression tests.

Nonlinear regression model for peak-failure strength of rockfill materials in general stress space

A nonlinear regression model for peak-failure strength prediction of rockfill materials is proposed. It is based on the relationship between the peak-failure stress ratio and the normalized confining pressure as well as the relationship between the normalized peak-failure stress ratio and the exponent function of the intermediate principal stress ratio. This model can well predict the variations of the peak-failure stress ratio with the initial confining pressure and the intermediate principal stress ratio for different rockfill materials under different general stress paths. Comparisons of the measured and predicted results show that the peak-failure strength under the constant-p' and constant-b path is larger than that under the constant-σ'_3 and constant-b path. The predictive capacity of the proposed model for the peakfailure stress ratio is better than that for the peak-failure friction angle.

A simple permanent deformation model of rockfill materials

Existing experimental results have shown that using a semi-log linear relationship between the permanent volumetric strain and cyclic number underestimates the volumetric deformation of rockfill materials with a large cyclic number, and that the error increases with the confining pressure. The existing permanent deformation models are not suitable for the seismic safety analysis of high dams during strong earthquakes. In this study, a series of large-scale triaxial cyclic loading tests of rockfill materials were performed, and a new permanent deformation model of rockfill materials was developed and validated with three kinds of rockfill materials. The results show that the proposed model can properly reflect the general features of the permanent deformation of rockfill materials. The main features of the model are as follows:(1) relations between the cyclic number and permanent volumetric/shear strain are described by hyperbolic functions, which can avoid underestimating the volumetric deformation occurring during strong earthquakes;(2) the model can capture the effect of the mean effective stress on the permanent volumetric strain, with greater confining pressure correlating to greater permanent volumetric deformation, and the permanent volumetric strain under low confining pressure near the dam crest can be well represented; and(3) the model can reflect the effect of the consolidation stress ratio on the permanent shear strain.

Packing,compressibility,and crushability of rockfill materials with polydisperse particle size distributions and implications for dam engineering

In rockfill dam engineering,particle breakage of rockfill materials is one of the major factors resulting in dam settlement.In this study,one-dimensional compression tests on a series of coarse granular materials with artificially-graded particle size distributions(PSDs)were carried out.The tests focused on understanding the role of initial PSDs in the dense packing density,compressibility and crushability of coarse granular materials.The effects of fractal dimension(D)and size polydispersity(θ)of PSDs were quantitatively analyzed.Two different loading stages were identified from the logarithms of the stress-strain relationships,with the turning point marked as the yield stress.A similar effect of initial PSDs was observed on the packing density and low-pressure modulus of coarse granular materials.The packing density and low-pressure modulus increased monotonically withθ,and their peak values were attained at a D value of approximately 2.2.However,there was no unique correspondence between the dense packing density and low-pressure modulus.The particle breakage was influenced differently by the initial PSDs,and it decreased with the values of D andθ.The emergence of the unique ultimate state was also identified from both the compression curves and PSDs of the samples after the tests.The potential implications of the test results in the design of both low and high rockfill dams were also demonstrated.

Calibration and performance of two different constitutive models for rockfill materials

In this paper, two different concepts for the constitutive modeling of the mechanical behavior of creep-sensitive rockfill materials are presented. Specifically, the performance of an extended generalized plasticity model proposed by Wang is compared with a simplified version of the hypoplastic constitutive model for weathered rockfill materials proposed by Bauer. Both models can reflect the influence of the mean stress on the incremental stiffness, the peak friction angle, and the dilatancy angle. The so-called solid hardness defined for a continuum description and originally introduced by Bauer is embedded in both models. Hydrochemical, thermal, and mechanical weathering are usually caused by environmental changes and are taken into account in a phenomenological description with an irreversible and time-dependent degradation of the solid hardness. A degradation of the solid hardness is usually accompanied by creep deformation of the stressed rockfill material. It is shown that appropriate modeling of creep deformation requires at least a unified description of the interaction between the time-dependent process of degradation of the solid hardness and the stress state. In this context, the solid hardness can be understood as a key parameter for describing the evolution of the state of weathering of the rockfill material. Particular attention is also paid to the necessary procedure for determining the constitutive constants of the two different constitutive models. Finally, the performance of the two different constitutive models is demonstrated by comparing the results obtained from numerical simulations with experimental data from the creep-sensitive rockfill material.

Generalized plasticity model considering grain crushing and anisotropy for rockfill materials

Rockfill materials have been widely used in the construction of rockfill dam,railway and highway subgrade due to its high filling density,good compaction performance,strong water permeability,small settlement deformation and high bearing capacity.A reasonable constitutive model for rockfill materials is very important for engineering computation and analysis,and has a great development space.Based on the crushing stress and spatial mobilized plane(SMP),a state parameter that can comprehensively reflect the anisotropy and grain crushing is proposed.This state parameter is used to improve the MPZ model(a modifed ZienkiewiczⅢmodel),so that a generalized plastic model is constructed to describe the stress and deformation characteristics of rockfill materials in engineering.The validity of the developed model is verified by a series of conventional triaxial tests with different inclination angles of the compaction plane.The variation trend of the constructed anisotropy indexωcan reflect the non monotonic variation of the deformation and strength of rockfill with the direction angle of large principal stress,so the model can reflect the obvious difference caused by the initial anisotropy of rockfill on the mechanical properties.

The Cemented Material Dam： A New, Environmentally Friendly Type of Dam

The first author proposed the concept of the cemented material dam （CMD） in 2009. This concept was aimed at building an environmentally friendly dam in a safer and more economical way for both the dam and the area downstream. The concept covers the cemented sand, gravel, and rock dam （CSGRD）, the rockfill concrete （RFC） dam （or the cemented rockfill dam, CRD）, and the cemented soil dam （CSD）. This paper summarizes the concept and principles of the CMD based on studies and practices in projects around the world. It also introduces new developments in the CSGRD, CRD, and CSD.

A generalized plasticity model for the stress-strain and creep behavior of rockfill materials

The generalized plasticity constitutive equations that simulate, in a unified manner, the stress-strain response and the creep behavior of rockfill materials are derived using the concept of elastoplasticity. A single yield surface is assumed to capture the onset of plastic strains with, however, two separate potential functions for the stress-induced plastic strains and the creep strains,respectively. The involved tensors and scalars are then specified directly, following the generalized plasticity method, to substantiate the constitutive equations. The model thus obtained is verified using triaxial compression experiments, true triaxial experiments and triaxial creep experiments. The effectiveness of the model is also demonstrated by a successful application in studying the behavior of a high concrete face rockfill dam(CFRD). It is found that for a high CFRD with a long construction period, neglecting the creep of rockfill materials during construction results in an underestimation of the deformation of the dam.The deformation and stress of the concrete slabs may also be considerably underestimated.

Dilatancy equation of rockfill material under the true triaxial stress condition

Rockfill material is widely used for construction of high rockfill dam due to its facility,economical cost,high strength and effective aseismatic property.It is provoked profoundly to propose a suitable constitutive model for a better application of this material.The dilatancy equation of rockfill material plays a significant role in the constitutive model.For the sake of simplicity,a dilatancy equation is established by the linear least square method on the basis of the rearranged data of rockfill material in the true triaxial tests.Based on the fact that the rearranged data at different initial confining pressures are aligned in a narrow band,the dilatancy behavior of rockfill material is independent of the initial confining pressure.However,different from the initial confining pressure,both the intermediate principal stress ratio and the specimen density exhibit a remarkable influence on the dilatancy behaviors of rockfill material.Furthermore,the predictions of the proposed dilatancy equation are in a good agreement with the rearranged test data of rockfill material at different specimen densities and stress paths.

A particle-breakage critical state model for rockfill material

Particle breakage has a significant influence on the stress-strain and strength behavior of rockfill material.A breakage critical state theory(BCST)was proposed to describe the evolution of particle breakage.The breakage critical state line in the breakage critical state theory was correlated with the breakage factor,which was fundamentally different from that of the original critical state theory.A simple elastoplastic constitutive model was developed for rockfill in the frame of BCST.An associated flow rule was adopted in this model.Isotropic,contractive and distortional hardening rules were suggested in view of the particle breakage.It was observed that the proposed model could well represent the complex deformation behaviors of rockfill material,such as the strain hardening,post-peak strain softening,volumetric contraction,volumetric expansion,and particle breakage under different initial confining pressures.

Modeling and behaviours of rockfill materials in three-dimensional stress space

A bounding surface model incorporating a unified nonlinear strength criterion is proposed.The proposed bounding surface model contains 9 model parameters,which can be determined from the conventional triaxial tests.The bounding surface model can reproduce such behaviours as the strain hardening,the post-peak strain softening,and the volumetric strain contraction and expansion.Based on the comparisons between the predictions and the test results,the proposed strength criterion and model can well reproduce the experimental results of the strength and stress-strain behaviours of rockfill material in three-dimensional stress space.The strength behaviour of rockfill material is summarized as:(a) the failure stress ratio decreases with the initial confining pressure on the meridian plane;(b) the failure deviatoric stress decreases with the Lode angle from 0o to 60o on the deviatoric plane.The stress ratio decreases with increasing one of such factors as the initial void ratio,the intermediate principal stress ratio and the minor principal stress at the same strain when the other factors are given.

A constitutive model for the state-dependent behaviors of rockfill material considering particle breakage

The particle breakage during specimen compaction had more significant influence on the position of the breakage critical-state line(BCSL)of Tacheng rockfill material(TRM)in the e-lnp’plane than the particle breakage during shearing,based on the large-scale triaxial compression tests on TRM in a wide range of densities and pressures.The state-dependent dilatancy and the plastic modulus were correlated to the breakage index,based on the formulations of the BCSL of TRM in the e-lnp’plane.The state-dependent model considering particle breakage was proposed for TRM within the framework of the generalized plasticity theory.The proposed model contained fourteen material constants.The test data of TRM from Group A were adopted to determine these material constants,while the test data from Group B were used independently to validate the model predictive capacity.The comparisons between model simulations and test data illustrated that the model with consideration of particle breakage could well represent the stress-strain behaviors of TRM,e.g.,the strain hardening and volumetric contraction behaviors at a loose state and the strain softening and volumetric expansion behaviors at a dense state,and also the particle breakage behaviors of TRM.

Hypoplastic constitutive modelling of the wetting induced creep of rockfill materials

Discrete element simulations of one-dimensional compression of breakable granular assemblies were performed to investigate the capability of the exponential compression equation suggested by Bauer.The relationship between the so-called solid hardness and the particle strength was studied so as to provide a physical background for the introduction of a time-dependent solid hardness.A hyperbolic flow rule,describing the relationship between the inclination of the strain path and the stress ratio during wetting,was proposed based on typical triaxial wetting experiments on two different rockfill materials.The flow rule was then extended and incorporated into the transformed stress based hypoplastic model to capture the direction of creep strains.Meanwhile,a new density factor was introduced to the extended model to take into account the dependence of the magnitude of creep strains on the packing density.The stiffness tensor given by the extended model was discussed and the flowchart for the integration of the constitutive equation was designed.The extended model was then embedded into a finite element program and used to simulate the triaxial compression and wetting experiments performed on the aforementioned rockfill materials.Good agreement between the model predictions and the measured results lends sufficient credibility to the extended model in reproducing the stress-stain behaviour under loading and the creep behaviour during wetting.The extended model and the finite element program were also used to investigate the deformation behaviour of an earth-rock dam at the end of construction and during first impounding.The familiar phenomena such as the wetting induced settlement of the upstream shell and the movement of the dam crest towards the upstream were successfully captured by the numerical model,which confirms the feasibility of applying the extended model to dam engineering in the future.

Hypoplastic constitutive modeling of wetting deformation of weathered rockfill materials

The wetting deformation of weathered rockfill materials has been attracting growing attention from both engineers and scientists.The importance of realistic predictions of wetting deformations for high earth and rockfill dams is a strong motivation to establish a suitable constitutive model.Recently,the hypoplastic constitutive model by Gudehus and Bauer was extended by introducing solid hardness depending on the state of weathering.The extended model takes into account the influence of the current density,the effective stress state,the rate of deformation,and the time dependent process of degradation of the solid hardness.In the present paper,the performance of this model is evaluated by comparing numerical simulations with experiments obtained from a water sensitive rockfill material.In particular,triaxial compression paths and creep deformation under deviatoric stress states are considered.Finally,the constitutive model proposed is used to study the influence of a degradation of the solid hardness on the long term behavior of a hypothetical fill dam.

Development of a constitutive model for rockfills and similar granular materials based on the disturbed state concept

Behavior of rockfills was investigated experimentally and theoretically.A series of standard triaxial compression tests were carried out on a quarried rockfill material at different stress levels.It was found that both the stress level and the shear stress ratio,like most of granular materials,controls the behavior of rockfill materials.At lower shear stress ratios the behavior is much more similar to a nonlinear elastic solid.When the shear stress goes further,the stressstrain curve shows an elasto-plastic behavior which suggests using the disturbed state concept to develop a constitutive model to predict the stress-strain behavior.The presented constitutive model complies reasonably with the experimental data.

考虑孔隙比影响的堆石料湿化试验及湿化模型

对某堆石坝的坝壳料进行了不同密实状态下的单线法三轴湿化试验,分析了湿化变形随围压、应力水平以及初始孔隙比的变化规律。结果表明:在围压和应力水平相同条件下,随着初始孔隙比的减小,堆石料湿化轴向应变和体积应变均明显降低;初始孔隙比对湿化应力剪胀规律影响不大,采用对数形式的湿化剪胀方程可对不同初始孔隙比条件下的湿化应力剪胀关系进行统一描述。对指数形式的湿化轴向应变经验模型进行修正,构建了考虑初始孔隙比及应力状态影响的湿化轴向应变计算模型,并联立湿化剪胀方程推导了湿化体积应变的计算公式,通过对三轴湿化试验结果进行模拟验证了该公式的合理性。

干湿循环作用下堆石料宏细观力学特性的离散元模拟研究

堆石料的物理力学特性在干湿循环作用下会发生明显劣化。基于堆石料颗粒三维扫描结果,建立了宽粒径范围的堆石料颗粒模板库。考虑干湿循环对颗粒强度、颗粒间接触模量和摩擦系数的影响,提出了一种考虑堆石颗粒干湿循环劣化的颗粒破碎模拟方案。在此基础上,采用FDM-DEM耦合方法对不同干湿循环作用下的堆石料试样进行一系列三轴压缩试验,讨论了在三轴压缩条件下干湿循环对堆石料宏细观力学特性的影响规律。结果表明:堆石料的初始模量和峰值强度随着干湿循环次数N的增加而呈非线性降低,干湿循环对体变曲线在初始阶段的剪缩和加载后期的剪胀有抑制作用,当N增大至某一值时,干湿循环对堆石料的宏观变形和强度的影响逐渐不明显。干湿循环次数越大,试样内部平均配位数越大,接触滑移比越大,试样内部的偏组构呈非线性减小,即各向异性程度在逐渐减小,这说明干湿循环对试样内部的各向异性发展有抑制作用。

堆石料本构模型对混凝土面板坝应力变形计算结果的影响研究

堆石料本构模型选择是影响混凝土面板坝应力变形计算结果的主要因素。以某典型面板坝为例,采用邓肯E-B非线性弹性模型和“南水”双屈服面弹塑性模型,对坝体填筑过程和蓄水过程进行了三维有限元模拟;研究了两种模型计算的坝体和面板的位移和应力分布差异;分析了两种模型计算结果呈现差异的原因。两种模型计算结果最显著的差异体现在两个方面:(1)“南水”模型计算的坝体沉降、面板挠度等位移指标小于E-B模型,其原因是“南水”模型计算的坝体小主应力和变形模量更高。(2)E-B模型计算结果显示蓄水后面板底部顺坡向受拉;而“南水”模型计算的面板顺坡向应力为全断面受压。前者是由E-B模型的各向同性弹性本质决定的,垫层料因水压力作用顺坡向膨胀,产生沿坡面向上的位移;后者是其F1屈服面持续扩张产生塑性体积收缩导致的,塑性体缩抵消了顺坡向弹性膨胀,使垫层料产生沿坡面向下的位移。

筑坝堆石料颗粒破碎及分形特性试验研究

为探究筑坝堆石料颗粒破碎现象,选取不同粗粒含量和含水量的堆石料作为研究对象,开展室内击实试验,分析土体的压实特性、颗粒破碎特性及分形特征,并揭示其力学响应机理。试验结果表明:随含水量的增加,堆石料的干密度先增大后减小。而最大干密度和最优含水量分别与粗粒含量呈现正相关和负相关。堆石料中出现明显的颗粒破碎现象,随粗粒含量和含水量的增加其颗粒破碎率随之增大。粗粒含量与含水量分别与分形维数成反比和正比关系,相较于含水量,粗粒含量对分形维数的影响更显著。

面板堆石坝含特细砂砂砾石填筑料碾压特性研究

阿尔塔什水利枢纽工程大坝主堆石区填筑料以砂砾石料为主,该地区河滩砂砾石料颗粒级配中的砂为特细砂,其在砂的级配中缺少中粗砂、级配不连续、保水性较差等特殊性级配料的特点导致其在施工过程中势必会影响到碾压的压实效果,给施工过程的质量控制带来很大难度。阐述了施工中通过对含特细砂砂砾石填筑料进行的不同加水量、不同厚度、不同碾压遍数及碾压机械等不同的碾压工艺参数进行试验检测、综合统计分析研究,探索出适合该工程的相关碾压施工参数标准,优化了施工碾压参数,提升了施工现场试验检测控制的时效性,为大坝填筑建设提供了稳定、可靠的施工参数,增强了坝体整体填筑的可靠性,为减小坝体沉降变形、提高大坝抗震安全储备和控制大坝施工质量等提供了有利条件。